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Numerical approximation of generalized Newtonian fluids using Powell-Sabin-Heindl elements. I: Theoretical estimates. (English) Zbl 1047.76040
Summary: In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell-Sabin-Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76A05 Non-Newtonian fluids
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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